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4 years ago

Which point could be on the line that is perpendicular to and passes through point K?

Mathematics

2 answers:

Ede4ka [16]4 years ago

3 0

It would be (2,2), because of the opposite reciprocal slope of a perpendicular line.

LUCKY_DIMON [66]4 years ago

3 0

Answer:

(2, 2)

Step-by-step explanation:

First we find the slope of the line through M and N. The coordinates of M are (2, 3) and the coordinates of N are (-3, 2). Using the formula for slope,

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-2}{2--3}=\frac{1}{5}$

For a line to be perpendicular to a given line, the slopes would be negative reciprocals (opposite signs and the fraction is flipped). This makes the slope of the perpendicular line -5/1.

The coordinates of point K are (3, -3). Going down 5 units and right 1 unit would put it at (4, -8). Going backwards, up 5 units and left 1 unit would be (2, 2). Thus (2, 2) is the point we are looking for.

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If f(x)=2x^3-6x^2-16x-20f(x)=2x *3 −6x *2−16x−20 and f(5)=0, then find all of the zeros of f(x)f(x) algebraically.

mihalych1998 [28]

The zeros of the cubic function f(x) = 2x³ - 6x² - 16x - 20 are given as follows:

x = 5, x = -1 + i, x = -1 - i.

<h3>How to obtain the solutions to the equation?</h3>

The equation is defined by the rule presented as follows:

f(x) = 2x³ - 6x² - 16x - 20.

One solution for the equation is given as follows:

x = 5.

Because f(5) = 0.

Then (x - 5) is a linear factor of the function f(x), which can be written as follows:

2x³ - 6x² - 16x - 20 = (ax² + bx + c)(x - 5).

This is because the product of a linear function and a quadratic function results in a cubic function.

Now we expand the right side to begin finding the coefficients of the quadratic function that we are going to solve to find the remaining zeros:

2x³ - 6x² - 16x - 20 = = ax³ + (b - 5a)x² + (c - 5b)x - 5c.

Then these coefficients are obtained comparing the left and the right side of the equality as follows:

a = 2.

-5c = -20 -> c = 4.

b = -6 + 5a = 4.

Hence the equation is:

2x² + 4x + 4.

Using a quadratic equation calculator, the remaining zeros are given as follows:

x = -1 + i.

x = -1 - i.

More can be learned about the solutions of an equation at brainly.com/question/25896797

#SPJ1

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1 year ago

Please help me out!!

solniwko [45]

The slope is 1 because it is parallel and y=x+b, so, 2=-3+b and b=5
y=x+5

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Natali [406]

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